Algebra and Trigonometry, 5th Edition

10.1 The Parabola

• Given an equation of a parabola, complete the square, if necessary, and then find the vertex, the focus, and the directrix and graph the parabola.

A conic section is formed when a right circular cone with two parts, called nappes, is intersected by a plane. One of four types of curves can be formed: a parabola, a circle, an ellipse, or a hyperbola.

Conic sections can be defined algebraically using second-degree equations of the form $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$. In addition, they can be defined geometrically as a set of points that satisfy certain conditions.

Parabolas

The graph of the quadratic function $f(x)=a{x}^2+bx+c$, $a\ne 0$, is a ...